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- 1. Chapter 6 Electronic Structure of Atoms Chemistry, The Central Science , 11th edition Theodore L. Brown; H. Eugene LeMay, Jr.; and Bruce E. Bursten John D. Bookstaver St. Charles Community College Cottleville, MO
- 2. Waves <ul><li>To understand the electronic structure of atoms, one must understand the nature of electromagnetic radiation. </li></ul><ul><li>The distance between corresponding points on adjacent waves is the wavelength ( ) . </li></ul>
- 3. Waves <ul><li>The number of waves passing a given point per unit of time is the frequency ( ) . </li></ul><ul><li>For waves traveling at the same velocity, the longer the wavelength, the smaller the frequency. </li></ul>
- 4. Electromagnetic Radiation <ul><li>All electromagnetic radiation travels at the same velocity: the speed of light ( c ), </li></ul><ul><li>3.00 10 8 m/s. </li></ul><ul><li>Therefore, </li></ul><ul><li>c = </li></ul>
- 5. The Nature of Energy <ul><li>The wave nature of light does not explain how an object can glow when its temperature increases. </li></ul><ul><li>Max Planck explained it by assuming that energy comes in packets called quanta . </li></ul>
- 6. The Nature of Energy <ul><li>Einstein used this assumption to explain the photoelectric effect. </li></ul><ul><li>He concluded that energy is proportional to frequency: </li></ul><ul><li>E = h </li></ul><ul><li>where h is Planck’s constant, 6.626 10 − 34 J-s. </li></ul>
- 7. The Nature of Energy <ul><li>Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light: </li></ul><ul><li>c = </li></ul><ul><li>E = h </li></ul>
- 8. The Nature of Energy <ul><li>Another mystery in the early 20th century involved the emission spectra observed from energy emitted by atoms and molecules. </li></ul>
- 9. The Nature of Energy <ul><li>For atoms and molecules one does not observe a continuous spectrum, as one gets from a white light source. </li></ul><ul><li>Only a line spectrum of discrete wavelengths is observed. </li></ul>
- 10. The Nature of Energy <ul><li>Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: </li></ul><ul><ul><li>Electrons in an atom can only occupy certain orbits (corresponding to certain energies). </li></ul></ul>
- 11. The Nature of Energy <ul><li>Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: </li></ul><ul><ul><li>Electrons in permitted orbits have specific, “allowed” energies; these energies will not be radiated from the atom. </li></ul></ul>
- 12. The Nature of Energy <ul><li>Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: </li></ul><ul><ul><li>Energy is only absorbed or emitted in such a way as to move an electron from one “allowed” energy state to another; the energy is defined by </li></ul></ul><ul><ul><li>E = h </li></ul></ul>
- 13. The Nature of Energy <ul><li>The energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the equation: </li></ul>where R H is the Rydberg constant, 2.18 10 − 18 J, and n i and n f are the initial and final energy levels of the electron. E = − R H ( ) 1 n f 2 1 n i 2 -
- 14. The Wave Nature of Matter <ul><li>Louis de Broglie posited that if light can have material properties, matter should exhibit wave properties. </li></ul><ul><li>He demonstrated that the relationship between mass and wavelength was </li></ul> = h mv
- 15. The Uncertainty Principle <ul><li>Heisenberg showed that the more precisely the momentum of a particle is known, the less precisely is its position known: </li></ul><ul><li>In many cases, our uncertainty of the whereabouts of an electron is greater than the size of the atom itself! </li></ul>( x ) ( mv ) h 4
- 16. Quantum Mechanics <ul><li>Erwin Schrödinger developed a mathematical treatment into which both the wave and particle nature of matter could be incorporated. </li></ul><ul><li>It is known as quantum mechanics . </li></ul>
- 17. Quantum Mechanics <ul><li>The wave equation is designated with a lower case Greek psi ( ). </li></ul><ul><li>The square of the wave equation, 2 , gives a probability density map of where an electron has a certain statistical likelihood of being at any given instant in time. </li></ul>
- 18. Quantum Numbers <ul><li>Solving the wave equation gives a set of wave functions, or orbitals , and their corresponding energies. </li></ul><ul><li>Each orbital describes a spatial distribution of electron density. </li></ul><ul><li>An orbital is described by a set of three quantum numbers . </li></ul>
- 19. Principal Quantum Number ( n ) <ul><li>The principal quantum number, n , describes the energy level on which the orbital resides. </li></ul><ul><li>The values of n are integers ≥ 1. </li></ul>
- 20. Angular Momentum Quantum Number ( l ) <ul><li>This quantum number defines the shape of the orbital. </li></ul><ul><li>Allowed values of l are integers ranging from 0 to n − 1. </li></ul><ul><li>We use letter designations to communicate the different values of l and, therefore, the shapes and types of orbitals. </li></ul>
- 21. Angular Momentum Quantum Number ( l ) f d p s Type of orbital 3 2 1 0 Value of l
- 22. Magnetic Quantum Number ( m l ) <ul><li>The magnetic quantum number describes the three-dimensional orientation of the orbital. </li></ul><ul><li>Allowed values of m l are integers ranging from - l to l : </li></ul><ul><li>− l ≤ m l ≤ l. </li></ul><ul><li>Therefore, on any given energy level, there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, etc. </li></ul>
- 23. Magnetic Quantum Number ( m l ) <ul><li>Orbitals with the same value of n form a shell . </li></ul><ul><li>Different orbital types within a shell are subshells . </li></ul>
- 24. s Orbitals <ul><li>The value of l for s orbitals is 0. </li></ul><ul><li>They are spherical in shape. </li></ul><ul><li>The radius of the sphere increases with the value of n. </li></ul>
- 25. s Orbitals <ul><li>Observing a graph of probabilities of finding an electron versus distance from the nucleus, we see that s orbitals possess n − 1 nodes , or regions where there is 0 probability of finding an electron. </li></ul>
- 26. p Orbitals <ul><li>The value of l for p orbitals is 1. </li></ul><ul><li>They have two lobes with a node between them. </li></ul>
- 27. d Orbitals <ul><li>The value of l for a d orbital is 2. </li></ul><ul><li>Four of the five d orbitals have 4 lobes; the other resembles a p orbital with a doughnut around the center. </li></ul>
- 28. Energies of Orbitals <ul><li>For a one-electron hydrogen atom, orbitals on the same energy level have the same energy. </li></ul><ul><li>That is, they are degenerate . </li></ul>
- 29. Energies of Orbitals <ul><li>As the number of electrons increases, though, so does the repulsion between them. </li></ul><ul><li>Therefore, in many-electron atoms, orbitals on the same energy level are no longer degenerate. </li></ul>
- 30. Spin Quantum Number, m s <ul><li>In the 1920s, it was discovered that two electrons in the same orbital do not have exactly the same energy. </li></ul><ul><li>The “spin” of an electron describes its magnetic field, which affects its energy. </li></ul>
- 31. Spin Quantum Number, m s <ul><li>This led to a fourth quantum number, the spin quantum number, m s . </li></ul><ul><li>The spin quantum number has only 2 allowed values: +1/2 and − 1/2. </li></ul>
- 32. Pauli Exclusion Principle <ul><li>No two electrons in the same atom can have exactly the same energy. </li></ul><ul><li>Therefore, no two electrons in the same atom can have identical sets of quantum numbers. </li></ul>
- 33. Electron Configurations <ul><li>This shows the distribution of all electrons in an atom. </li></ul><ul><li>Each component consists of </li></ul><ul><ul><li>A number denoting the energy level, </li></ul></ul>
- 34. Electron Configurations <ul><li>This shows the distribution of all electrons in an atom </li></ul><ul><li>Each component consists of </li></ul><ul><ul><li>A number denoting the energy level, </li></ul></ul><ul><ul><li>A letter denoting the type of orbital, </li></ul></ul>
- 35. Electron Configurations <ul><li>This shows the distribution of all electrons in an atom. </li></ul><ul><li>Each component consists of </li></ul><ul><ul><li>A number denoting the energy level, </li></ul></ul><ul><ul><li>A letter denoting the type of orbital, </li></ul></ul><ul><ul><li>A superscript denoting the number of electrons in those orbitals. </li></ul></ul>
- 36. Orbital Diagrams <ul><li>Each box in the diagram represents one orbital. </li></ul><ul><li>Half-arrows represent the electrons. </li></ul><ul><li>The direction of the arrow represents the relative spin of the electron. </li></ul>
- 37. Hund’s Rule <ul><li>“ For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized.” </li></ul>
- 38. Periodic Table <ul><li>We fill orbitals in increasing order of energy. </li></ul><ul><li>Different blocks on the periodic table (shaded in different colors in this chart) correspond to different types of orbitals. </li></ul>
- 39. Some Anomalies <ul><li>Some irregularities occur when there are enough electrons to half-fill s and d orbitals on a given row. </li></ul>
- 40. Some Anomalies <ul><li>For instance, the electron configuration for copper is </li></ul><ul><li>[Ar] 4 s 1 3 d 5 </li></ul><ul><li>rather than the expected </li></ul><ul><li>[Ar] 4 s 2 3 d 4 . </li></ul>
- 41. Some Anomalies <ul><li>This occurs because the 4 s and 3 d orbitals are very close in energy. </li></ul><ul><li>These anomalies occur in f -block atoms, as well. </li></ul>

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